Abstract:

This article reports on a study carried out with a class of 25 pupils in the 3rd year of schooling, aged eight to nine, focusing on the topic of “Numbers”, specifically “Mental Calculation”. The main purpose was to explore how pupils could strengthen their number sense and mental calculation strategies by working with non-verbal representations and numerical properties. The study was guided by the following research question: How does understanding numerical properties contribute to the development of mental calculation in 3rd-year pupils?.

A mixed-methods approach was adopted, combining several techniques and instruments. These included pre- and post-tests, interviews with the class teacher before and after the intervention, direct observation of the sessions, and analysis of the written work produced by the pupils.

Across eight training sessions, pupils worked with “Papy’s Minicalculator” and arrow notation to explore number sense and engage in mental calculation tasks. At the outset, many pupils showed limited confidence and flexibility in this area, which made the progression observed particularly meaningful.

Throughout the training sessions, pupils explored the topic of “Mental Calculation” in a gradual and engaging way. Through a range of activities — such as using Papy’s Minicalculator, discovering different ways of representing numbers, becoming familiar with arrow language, and solving small addition and subtraction challenges — an atmosphere of experimentation and curiosity was created. The researcher aimed to ensure that these experiences were both motivating and meaningful, making use of hands-on materials and tasks that captured pupils’ interest. This helped them take an active role in their learning, deepen their understanding of number, and develop mental calculation strategies naturally and progressively within the everyday life of the classroom.

The comparison between the pre- and post-test results showed a clear improvement: the average score rose from 30% to 51%. The class teacher also highlighted the progress made, commenting that “all the activities carried out this year were very interesting and important for the development of mental calculation”.

In light of the results, we conclude that reinforcing number sense and helping pupils recognise and use numerical properties had a positive impact on their mental calculation skills. The materials and approaches used in the sessions proved to be valuable and appropriate for this age group.

Keywords:

Mental calculation, numerical properties, non-verbal representations, 3rd year of schooling.